The conventional industrial techniques for measuring viscosity do not make it possible to carry out measurements on very thin films, for example films with a thickness of less than 10 micrometers.
For very thin films, various laboratory solutions have been proposed, notably measurement of the progressive leveling of a periodic pattern imposed in the layer of viscous film. Its principle is as follows: a periodic initial pattern is established in the film, for example a network of identical parallel linear ridges which are regularly spaced, each having a rectangular cross section; this pattern is for example impressed in the film at a temperature at which the film is viscous; the solidified impressed pattern is measured precisely, for example by means of an atomic force microscope; the spatial profile of the pattern is decomposed into a Fourier series; the film is heated to the temperature at which the viscosity is intended to be measured, for a determined time, which may be called the baking time; the pattern tends to become leveled more or less depending on the viscosity of the film at the measurement temperature; the film is cooled again in order to make it solid; the new geometrical profile of the periodic network is measured; this profile is decomposed into a Fourier series; calculation based on the fundamental coefficient of each of the two Fourier series makes it possible to determine a characteristic term, which is the ratio between the viscosity and the surface tension, if the average thickness of the film, the spatial period of the pattern and the time for which the pattern has been subjected to the measurement temperature are known; since the surface tension can be measured independently by other techniques, the viscosity can be calculated.
If the respective amplitudes of the fundamental coefficient of each of the two Fourier series are denoted as a0 and aflu, it is possible to write:aflu/a0=exp(−tflu/τ)where tflu is the baking time and τ is a time constant associated with the viscosity, which can be writtenτ=3η(1/γh03)(λ/2π)4 where η is the viscosity, γ is the surface tension, λ is the spatial period of the periodic pattern (the period which defines the fundamental frequency of the Fourier series) and h0 is the average thickness of the layer.
One of the drawbacks of this method is the fact that measuring the viscosity by determining the ratio aflu/a0 makes sense only if this ratio is not too close to 1 and not too close to 0, which is equivalent to saying that if the periodic pattern has almost not moved during the baking time, or if the pattern is almost flattened after the baking, the measurement inaccuracies are too great to achieve a reliable determination of the viscosity.
It is therefore necessary to determine in advance a network geometry and a baking time and which will lead to a ratio aflu/a0 that is acceptable, for example not too far from 0.5, which means that it is necessary to know the likely value of the viscosity in advance with a good approximation. It is furthermore necessary for the selected baking time to be compatible with the possibilities of practical experimentation: a fairly long time in order to allow stabilization of the temperature of the film, but a fairly short time (less than one hour) in order to allow reasonable experimentation.